This post discusses dependent and independent variables.  It provides an example of a single independent and dependent variable and a case with two independent and one dependent variable.  It discusses group comparison, and that the mean of a group along is not a sufficient measure to determine the most common values.

Dependent and Independent Variables

A scenario containing an independent and dependent variable is a dataset containing speed and stopping distance (Anonomous, 2017).  The cars dataset contains fifty observations containing speed (measured in miles per hour) and distance (measured in feet).  In this dataset speed is the independent variable while distance is dependent.  The ratio between the variables is non-linear.  As speed increases distance increases at a greater rate.

A variation of the cars dataset that would include two independent variables is if the type of brake was included.  The values for brake would be drum, disk, and antilock braking system.  Distance would continue to be a dependent variable.

Intra and Inter Group Variance

When looking at the performance of two groups on a given task, one speaks of two kinds of variance (between-groups and within-groups). What does each represent? Be sure to discuss this answer in terms of variance and not research designs.

Variance measured within a group is a means of determining the level of dispersion of values within a sample.  Variance between groups is related to analysis of variance (ANOVA) (Babbie, Halley, & Zaino, 2007).  The basic idea is that if two groups are randomly drawn from the same sample their variance should be similar and should be similar to the variance of the population in general.

Manufacturing Process Comparison

When evaluating two processes, it is important to understand the distribution when attempting to determine performance.  Given the example of process A having a mean of 82.5 and process B having a mean of 78.5 one cannot infer that process A is generally better than A.  If process A has a high degree of variance (especially with high valued outliers) it could produce consistently lower values than process B.  The occasional high value would offset the normal low valued output.

References

Anonomous. (2017). R: Speed and Stopping Distances of Cars.   Retrieved from https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/cars.html

Babbie, E. R., Halley, F., & Zaino, J. (2007). Adventures in social research: data analysis using SPSS 14.0 and 15.0 for Windows: Pine Forge Press.